A Formal Treatment of Sequential Ignorability

Taking a rigorous formal approach, we consider sequential decision problems involving observable variables, unobservable variables, and action variables. We can typically assume the property of extended stability, which allows identification (by means of G-computation) of the consequence of a specified treatment strategy if the unobserved variables are, in fact, observed - but not generally otherwise. However, under certain additional special conditions we can infer simple stability (or sequential ignorability), which supports G-computation based on the observed variables alone. One such additional condition is sequential randomization, where the unobserved variables essentially behave as random noise in their effects on the actions. Another is sequential irrelevance, where the unobserved variables do not influence future observed variables. In the latter case, to deduce sequential ignorability in full generality requires additional positivity conditions. We show here that these positivity conditions are not required when all variables are discrete.Comment: 25 pages, 5 figures, 1 tabl

Do CDS spreads reflect default risks? Evidence from UK bank bailouts

CDS spreads are generally considered to reflect the credit risks of their reference entities. However, CDS spreads of the major UK banks remained relatively stable in response to the recent credit crisis. We suggest that this can be explained by changes in loss given default (LGD). To obtain the result we first derive the probabilities of default from stock option prices and then determine the LGD consistent with actual CDS spreads. Our results reveal a significant decrease in the LGD of bailed out banks over the observed period in contrast to banks which were not bailed out and non-financial companies

Network protocol scalability via a topological Kadanoff transformation

A natural hierarchical framework for network topology abstraction is presented based on an analogy with the Kadanoff transformation and renormalisation group in theoretical physics. Some properties of the renormalisation group bear similarities to the scalability properties of network routing protocols (interactions). Central to our abstraction are two intimately connected and complementary path diversity units: simple cycles, and cycle adjacencies. A recursive network abstraction procedure is presented, together with an associated generic recursive routing protocol family that offers many desirable features.Comment: 4 pages, 5 figures, PhysComNet 2008 workshop submissio

Learning Bayesian Networks with the Saiyan algorithm

Some structure learning algorithms have proven to be effective in reconstructing hypothetical Bayesian Network (BN) graphs from synthetic data. However, in their mission to maximise a scoring function, many become conservative and minimise edges discovered. While simplicity is desired, the output is often a graph that consists of multiple independent graphical fragments or variables that do not enable full propagation of evidence. While this is not a problem in theory, it can be a problem in practice. This paper presents a novel unconventional heuristic local-search structure learning algorithm, called Saiyan, which returns a directed acyclic graph that enables full propagation of evidence. Forcing the algorithm to connect all data variables and to direct all of the edges discovered implies that the additional forced arcs are not expected to be correct at the rate of those identified unrestrictedly, and this evidently has a negative impact on the evaluation score of the discovered graph. Still, based on both synthetic and real-world experiments, the Saiyan algorithm demonstrates competitive performance relative to other state-of-the-art constraint-based, score-based, and hybrid structure learning algorithms